Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B

Percentage Accurate: 99.8% → 99.8%

Time: 16.9s

Alternatives: 18

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (((((x * log(y)) + z) + t) + a) + ((b - 0.5d0) * log(c))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((x * Math.log(y)) + z) + t) + a) + ((b - 0.5) * Math.log(c))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return (((((x * math.log(y)) + z) + t) + a) + ((b - 0.5) * math.log(c))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(Float64(Float64(Float64(x * log(y)) + z) + t) + a) + Float64(Float64(b - 0.5) * log(c))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (((((x * log(y)) + z) + t) + a) + ((b - 0.5) * log(c))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(N[(N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision] + t), $MachinePrecision] + a), $MachinePrecision] + N[(N[(b - 0.5), $MachinePrecision] * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (fma y i (fma (+ b -0.5) (log c) (+ z (fma x (log y) (+ t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return fma(y, i, fma((b + -0.5), log(c), (z + fma(x, log(y), (t + a)))));
}

Julia

function code(x, y, z, t, a, b, c, i)
	return fma(y, i, fma(Float64(b + -0.5), log(c), Float64(z + fma(x, log(y), Float64(t + a)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(y * i + N[(N[(b + -0.5), $MachinePrecision] * N[Log[c], $MachinePrecision] + N[(z + N[(x * N[Log[y], $MachinePrecision] + N[(t + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Step-by-step derivation

   1. associate-+l+ 99.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right)} \]

   2. +-commutative 99.4%

      \[\leadsto \color{blue}{\left(a + \left(\left(x \cdot \log y + z\right) + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   3. associate-+l+ 99.4%

      \[\leadsto \left(a + \color{blue}{\left(x \cdot \log y + \left(z + t\right)\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   4. associate-+r+ 99.4%

      \[\leadsto \color{blue}{\left(\left(a + x \cdot \log y\right) + \left(z + t\right)\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   5. +-commutative 99.4%

      \[\leadsto \left(\left(a + x \cdot \log y\right) + \color{blue}{\left(t + z\right)}\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   6. +-commutative 99.4%

      \[\leadsto \left(\color{blue}{\left(x \cdot \log y + a\right)} + \left(t + z\right)\right) + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   7. associate-+l+ 99.4%

      \[\leadsto \color{blue}{\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)} + \left(\left(b - 0.5\right) \cdot \log c + y \cdot i\right) \]

   8. associate-+l+ 99.4%

      \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i} \]

   9. +-commutative 99.4%

      \[\leadsto \color{blue}{y \cdot i + \left(\left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

   10. fma-define 99.8%

       \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right) + \left(b - 0.5\right) \cdot \log c\right)} \]

   11. +-commutative 99.8%

       \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\left(b - 0.5\right) \cdot \log c + \left(\left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

   12. fma-define 99.8%

       \[\leadsto \mathsf{fma}\left(y, i, \color{blue}{\mathsf{fma}\left(b - 0.5, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)}\right) \]

   13. sub-neg 99.8%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(\color{blue}{b + \left(-0.5\right)}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

   14. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + \color{blue}{-0.5}, \log c, \left(\left(x \cdot \log y + a\right) + t\right) + z\right)\right) \]

   15. +-commutative 99.8%

       \[\leadsto \mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, \color{blue}{z + \left(\left(x \cdot \log y + a\right) + t\right)}\right)\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, i, \mathsf{fma}\left(b + -0.5, \log c, z + \mathsf{fma}\left(x, \log y, t + a\right)\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 94.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+52} \lor \neg \left(b - 0.5 \leq 10^{+142}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + -0.5 \cdot \log c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= (- b 0.5) -2e+52) (not (<= (- b 0.5) 1e+142)))
   (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))
   (+ (* y i) (+ (+ a (+ t (+ z (* x (log y))))) (* -0.5 (log c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -2e+52) || !((b - 0.5) <= 1e+142)) {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + (-0.5 * log(c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (((b - 0.5d0) <= (-2d+52)) .or. (.not. ((b - 0.5d0) <= 1d+142))) then
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    else
        tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + ((-0.5d0) * log(c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (((b - 0.5) <= -2e+52) || !((b - 0.5) <= 1e+142)) {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	} else {
		tmp = (y * i) + ((a + (t + (z + (x * Math.log(y))))) + (-0.5 * Math.log(c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if ((b - 0.5) <= -2e+52) or not ((b - 0.5) <= 1e+142):
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	else:
		tmp = (y * i) + ((a + (t + (z + (x * math.log(y))))) + (-0.5 * math.log(c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((Float64(b - 0.5) <= -2e+52) || !(Float64(b - 0.5) <= 1e+142))
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	else
		tmp = Float64(Float64(y * i) + Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(-0.5 * log(c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (((b - 0.5) <= -2e+52) || ~(((b - 0.5) <= 1e+142)))
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	else
		tmp = (y * i) + ((a + (t + (z + (x * log(y))))) + (-0.5 * log(c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[N[(b - 0.5), $MachinePrecision], -2e+52], N[Not[LessEqual[N[(b - 0.5), $MachinePrecision], 1e+142]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.5 * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 b #s(literal 1/2 binary64)) < -2e52 or 1.00000000000000005e142 < (-.f64 b #s(literal 1/2 binary64))

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 95.0%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   if -2e52 < (-.f64 b #s(literal 1/2 binary64)) < 1.00000000000000005e142

   1. Initial program 99.4%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in b around 0 98.6%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{-0.5 \cdot \log c}\right) + y \cdot i \]
   4. Step-by-step derivation

      1. *-commutative 98.6%

         \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\log c \cdot -0.5}\right) + y \cdot i \]

   5. Simplified 98.6%

      \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\log c \cdot -0.5}\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - 0.5 \leq -2 \cdot 10^{+52} \lor \neg \left(b - 0.5 \leq 10^{+142}\right):\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + -0.5 \cdot \log c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (+ (+ (+ a (+ t (+ z (* x (log y))))) (* (log c) (- b 0.5))) (* y i)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5))) + (y * i);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5d0))) + (y * i)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((a + (t + (z + (x * Math.log(y))))) + (Math.log(c) * (b - 0.5))) + (y * i);
}

Python

def code(x, y, z, t, a, b, c, i):
	return ((a + (t + (z + (x * math.log(y))))) + (math.log(c) * (b - 0.5))) + (y * i)

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(Float64(a + Float64(t + Float64(z + Float64(x * log(y))))) + Float64(log(c) * Float64(b - 0.5))) + Float64(y * i))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = ((a + (t + (z + (x * log(y))))) + (log(c) * (b - 0.5))) + (y * i);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Add Preprocessing

3. Final simplification 99.4%

   \[\leadsto \left(\left(a + \left(t + \left(z + x \cdot \log y\right)\right)\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i \]
4. Add Preprocessing

Alternative 4: 72.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-151}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-82}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + b \cdot \log c\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+97}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (* x (+ (log y) (/ z x))))))
   (if (<= x -1.8e+184)
     t_1
     (if (<= x 9.6e-151)
       (+ a (+ t (+ z (* (log c) (- b 0.5)))))
       (if (<= x 8.8e-82)
         (+ (* y i) (+ a (+ t (* b (log c)))))
         (if (<= x 2.4e+97) (+ (* y i) (+ a (+ z t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (x * (log(y) + (z / x)));
	double tmp;
	if (x <= -1.8e+184) {
		tmp = t_1;
	} else if (x <= 9.6e-151) {
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	} else if (x <= 8.8e-82) {
		tmp = (y * i) + (a + (t + (b * log(c))));
	} else if (x <= 2.4e+97) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * i) + (x * (log(y) + (z / x)))
    if (x <= (-1.8d+184)) then
        tmp = t_1
    else if (x <= 9.6d-151) then
        tmp = a + (t + (z + (log(c) * (b - 0.5d0))))
    else if (x <= 8.8d-82) then
        tmp = (y * i) + (a + (t + (b * log(c))))
    else if (x <= 2.4d+97) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (x * (Math.log(y) + (z / x)));
	double tmp;
	if (x <= -1.8e+184) {
		tmp = t_1;
	} else if (x <= 9.6e-151) {
		tmp = a + (t + (z + (Math.log(c) * (b - 0.5))));
	} else if (x <= 8.8e-82) {
		tmp = (y * i) + (a + (t + (b * Math.log(c))));
	} else if (x <= 2.4e+97) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (x * (math.log(y) + (z / x)))
	tmp = 0
	if x <= -1.8e+184:
		tmp = t_1
	elif x <= 9.6e-151:
		tmp = a + (t + (z + (math.log(c) * (b - 0.5))))
	elif x <= 8.8e-82:
		tmp = (y * i) + (a + (t + (b * math.log(c))))
	elif x <= 2.4e+97:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(z / x))))
	tmp = 0.0
	if (x <= -1.8e+184)
		tmp = t_1;
	elseif (x <= 9.6e-151)
		tmp = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	elseif (x <= 8.8e-82)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(b * log(c)))));
	elseif (x <= 2.4e+97)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (x * (log(y) + (z / x)));
	tmp = 0.0;
	if (x <= -1.8e+184)
		tmp = t_1;
	elseif (x <= 9.6e-151)
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	elseif (x <= 8.8e-82)
		tmp = (y * i) + (a + (t + (b * log(c))));
	elseif (x <= 2.4e+97)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8e+184], t$95$1, If[LessEqual[x, 9.6e-151], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.8e-82], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e+97], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.80000000000000007e184 or 2.4e97 < x

   1. Initial program 98.3%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 62.8%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 62.8%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 62.8%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 62.8%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 62.8%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 62.8%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in x around inf 59.3%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{x \cdot \log y}{z}}\right) + y \cdot i \]
   7. Step-by-step derivation

      1. associate-*r/ 59.3%

         \[\leadsto z \cdot \left(1 + \color{blue}{x \cdot \frac{\log y}{z}}\right) + y \cdot i \]

   8. Simplified 59.3%

      \[\leadsto z \cdot \left(1 + \color{blue}{x \cdot \frac{\log y}{z}}\right) + y \cdot i \]

   9. Taylor expanded in x around inf 79.2%

      \[\leadsto \color{blue}{x \cdot \left(\log y + \frac{z}{x}\right)} + y \cdot i \]

   if -1.80000000000000007e184 < x < 9.6e-151

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.8%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in y around 0 83.7%

      \[\leadsto \color{blue}{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)} \]

   if 9.6e-151 < x < 8.79999999999999943e-82

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in b around inf 89.9%

      \[\leadsto \left(a + \left(t + \color{blue}{b \cdot \log c}\right)\right) + y \cdot i \]
   5. Step-by-step derivation

      1. *-commutative 89.9%

         \[\leadsto \left(a + \left(t + \color{blue}{\log c \cdot b}\right)\right) + y \cdot i \]

   6. Simplified 89.9%

      \[\leadsto \left(a + \left(t + \color{blue}{\log c \cdot b}\right)\right) + y \cdot i \]

   if 8.79999999999999943e-82 < x < 2.4e97

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.6%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in z around inf 76.4%

      \[\leadsto \left(a + \left(t + \color{blue}{z}\right)\right) + y \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+184}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-151}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-82}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + b \cdot \log c\right)\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+97}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-135}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+96}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (let* ((t_1 (+ (* y i) (* x (+ (log y) (/ z x))))))
   (if (<= x -1.9e+184)
     t_1
     (if (<= x 1.7e-135)
       (+ a (+ t (+ z (* (log c) (- b 0.5)))))
       (if (<= x 3.3e+96) (+ (* y i) (+ a (+ z t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (x * (log(y) + (z / x)));
	double tmp;
	if (x <= -1.9e+184) {
		tmp = t_1;
	} else if (x <= 1.7e-135) {
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	} else if (x <= 3.3e+96) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * i) + (x * (log(y) + (z / x)))
    if (x <= (-1.9d+184)) then
        tmp = t_1
    else if (x <= 1.7d-135) then
        tmp = a + (t + (z + (log(c) * (b - 0.5d0))))
    else if (x <= 3.3d+96) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double t_1 = (y * i) + (x * (Math.log(y) + (z / x)));
	double tmp;
	if (x <= -1.9e+184) {
		tmp = t_1;
	} else if (x <= 1.7e-135) {
		tmp = a + (t + (z + (Math.log(c) * (b - 0.5))));
	} else if (x <= 3.3e+96) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	t_1 = (y * i) + (x * (math.log(y) + (z / x)))
	tmp = 0
	if x <= -1.9e+184:
		tmp = t_1
	elif x <= 1.7e-135:
		tmp = a + (t + (z + (math.log(c) * (b - 0.5))))
	elif x <= 3.3e+96:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	t_1 = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(z / x))))
	tmp = 0.0
	if (x <= -1.9e+184)
		tmp = t_1;
	elseif (x <= 1.7e-135)
		tmp = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	elseif (x <= 3.3e+96)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	t_1 = (y * i) + (x * (log(y) + (z / x)));
	tmp = 0.0;
	if (x <= -1.9e+184)
		tmp = t_1;
	elseif (x <= 1.7e-135)
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	elseif (x <= 3.3e+96)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := Block[{t$95$1 = N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e+184], t$95$1, If[LessEqual[x, 1.7e-135], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.3e+96], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.9000000000000001e184 or 3.29999999999999984e96 < x

   1. Initial program 98.3%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 62.8%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 62.8%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 62.8%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 62.8%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 62.8%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 62.8%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in x around inf 59.3%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{x \cdot \log y}{z}}\right) + y \cdot i \]
   7. Step-by-step derivation

      1. associate-*r/ 59.3%

         \[\leadsto z \cdot \left(1 + \color{blue}{x \cdot \frac{\log y}{z}}\right) + y \cdot i \]

   8. Simplified 59.3%

      \[\leadsto z \cdot \left(1 + \color{blue}{x \cdot \frac{\log y}{z}}\right) + y \cdot i \]

   9. Taylor expanded in x around inf 79.2%

      \[\leadsto \color{blue}{x \cdot \left(\log y + \frac{z}{x}\right)} + y \cdot i \]

   if -1.9000000000000001e184 < x < 1.69999999999999995e-135

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.8%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in y around 0 83.4%

      \[\leadsto \color{blue}{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)} \]

   if 1.69999999999999995e-135 < x < 3.29999999999999984e96

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 95.2%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in z around inf 74.0%

      \[\leadsto \left(a + \left(t + \color{blue}{z}\right)\right) + y \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+184}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-135}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+96}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+189} \lor \neg \left(x \leq 5.2 \cdot 10^{+141}\right):\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.15e+189) (not (<= x 5.2e+141)))
   (+ (* y i) (* x (+ (log y) (/ z x))))
   (+ (* y i) (+ a (+ t (+ z (* (log c) (- b 0.5))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.15e+189) || !(x <= 5.2e+141)) {
		tmp = (y * i) + (x * (log(y) + (z / x)));
	} else {
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.15d+189)) .or. (.not. (x <= 5.2d+141))) then
        tmp = (y * i) + (x * (log(y) + (z / x)))
    else
        tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.15e+189) || !(x <= 5.2e+141)) {
		tmp = (y * i) + (x * (Math.log(y) + (z / x)));
	} else {
		tmp = (y * i) + (a + (t + (z + (Math.log(c) * (b - 0.5)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.15e+189) or not (x <= 5.2e+141):
		tmp = (y * i) + (x * (math.log(y) + (z / x)))
	else:
		tmp = (y * i) + (a + (t + (z + (math.log(c) * (b - 0.5)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.15e+189) || !(x <= 5.2e+141))
		tmp = Float64(Float64(y * i) + Float64(x * Float64(log(y) + Float64(z / x))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.15e+189) || ~((x <= 5.2e+141)))
		tmp = (y * i) + (x * (log(y) + (z / x)));
	else
		tmp = (y * i) + (a + (t + (z + (log(c) * (b - 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.15e+189], N[Not[LessEqual[x, 5.2e+141]], $MachinePrecision]], N[(N[(y * i), $MachinePrecision] + N[(x * N[(N[Log[y], $MachinePrecision] + N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.14999999999999999e189 or 5.1999999999999999e141 < x

   1. Initial program 98.2%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 64.5%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 64.4%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 64.4%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 64.4%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 64.4%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 64.4%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in x around inf 60.5%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{x \cdot \log y}{z}}\right) + y \cdot i \]
   7. Step-by-step derivation

      1. associate-*r/ 60.5%

         \[\leadsto z \cdot \left(1 + \color{blue}{x \cdot \frac{\log y}{z}}\right) + y \cdot i \]

   8. Simplified 60.5%

      \[\leadsto z \cdot \left(1 + \color{blue}{x \cdot \frac{\log y}{z}}\right) + y \cdot i \]

   9. Taylor expanded in x around inf 82.9%

      \[\leadsto \color{blue}{x \cdot \left(\log y + \frac{z}{x}\right)} + y \cdot i \]

   if -2.14999999999999999e189 < x < 5.1999999999999999e141

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.0%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{+189} \lor \neg \left(x \leq 5.2 \cdot 10^{+141}\right):\\ \;\;\;\;y \cdot i + x \cdot \left(\log y + \frac{z}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \left(\log y + i \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-135}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+80}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -3.6e+185)
   (* x (+ (log y) (* i (/ y x))))
   (if (<= x 1.4e-135)
     (+ a (+ t (+ z (* (log c) (- b 0.5)))))
     (if (<= x 3.8e+80)
       (+ (* y i) (+ a (+ z t)))
       (+ a (+ t (+ z (* x (log y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -3.6e+185) {
		tmp = x * (log(y) + (i * (y / x)));
	} else if (x <= 1.4e-135) {
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	} else if (x <= 3.8e+80) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = a + (t + (z + (x * log(y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-3.6d+185)) then
        tmp = x * (log(y) + (i * (y / x)))
    else if (x <= 1.4d-135) then
        tmp = a + (t + (z + (log(c) * (b - 0.5d0))))
    else if (x <= 3.8d+80) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = a + (t + (z + (x * log(y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -3.6e+185) {
		tmp = x * (Math.log(y) + (i * (y / x)));
	} else if (x <= 1.4e-135) {
		tmp = a + (t + (z + (Math.log(c) * (b - 0.5))));
	} else if (x <= 3.8e+80) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = a + (t + (z + (x * Math.log(y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -3.6e+185:
		tmp = x * (math.log(y) + (i * (y / x)))
	elif x <= 1.4e-135:
		tmp = a + (t + (z + (math.log(c) * (b - 0.5))))
	elif x <= 3.8e+80:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = a + (t + (z + (x * math.log(y))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -3.6e+185)
		tmp = Float64(x * Float64(log(y) + Float64(i * Float64(y / x))));
	elseif (x <= 1.4e-135)
		tmp = Float64(a + Float64(t + Float64(z + Float64(log(c) * Float64(b - 0.5)))));
	elseif (x <= 3.8e+80)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -3.6e+185)
		tmp = x * (log(y) + (i * (y / x)));
	elseif (x <= 1.4e-135)
		tmp = a + (t + (z + (log(c) * (b - 0.5))));
	elseif (x <= 3.8e+80)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = a + (t + (z + (x * log(y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -3.6e+185], N[(x * N[(N[Log[y], $MachinePrecision] + N[(i * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.4e-135], N[(a + N[(t + N[(z + N[(N[Log[c], $MachinePrecision] * N[(b - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e+80], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.60000000000000029e185

   1. Initial program 96.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 60.2%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 60.0%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around 0 60.0%

      \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{-0.5 \cdot \frac{\log c}{z}}\right)\right)\right)\right) + y \cdot i \]
   7. Step-by-step derivation

      1. associate-*r/ 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\frac{-0.5 \cdot \log c}{z}}\right)\right)\right)\right) + y \cdot i \]

      2. *-commutative 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\color{blue}{\log c \cdot -0.5}}{z}\right)\right)\right)\right) + y \cdot i \]

   8. Simplified 60.0%

      \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\frac{\log c \cdot -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   9. Taylor expanded in x around inf 79.7%

      \[\leadsto \color{blue}{x \cdot \log y} + y \cdot i \]

   10. Taylor expanded in x around inf 79.6%

       \[\leadsto \color{blue}{x \cdot \left(\log y + \frac{i \cdot y}{x}\right)} \]
   11. Step-by-step derivation

       1. associate-/l* 82.7%

          \[\leadsto x \cdot \left(\log y + \color{blue}{i \cdot \frac{y}{x}}\right) \]

   12. Simplified 82.7%

       \[\leadsto \color{blue}{x \cdot \left(\log y + i \cdot \frac{y}{x}\right)} \]

   if -3.60000000000000029e185 < x < 1.40000000000000012e-135

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.8%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in y around 0 83.4%

      \[\leadsto \color{blue}{a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)} \]

   if 1.40000000000000012e-135 < x < 3.79999999999999997e80

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.6%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in z around inf 75.7%

      \[\leadsto \left(a + \left(t + \color{blue}{z}\right)\right) + y \cdot i \]

   if 3.79999999999999997e80 < x

   1. Initial program 99.6%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.9%

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} \]

   4. Taylor expanded in x around inf 73.7%

      \[\leadsto a + \left(t + \left(z + \color{blue}{x \cdot \log y}\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+185}:\\ \;\;\;\;x \cdot \left(\log y + i \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-135}:\\ \;\;\;\;a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{+80}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(\log y + i \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-137}:\\ \;\;\;\;a + \left(t + \left(z + b \cdot \log c\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+80}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -4.6e+184)
   (* x (+ (log y) (* i (/ y x))))
   (if (<= x 6.2e-137)
     (+ a (+ t (+ z (* b (log c)))))
     (if (<= x 4.2e+80)
       (+ (* y i) (+ a (+ z t)))
       (+ a (+ t (+ z (* x (log y)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -4.6e+184) {
		tmp = x * (log(y) + (i * (y / x)));
	} else if (x <= 6.2e-137) {
		tmp = a + (t + (z + (b * log(c))));
	} else if (x <= 4.2e+80) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = a + (t + (z + (x * log(y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-4.6d+184)) then
        tmp = x * (log(y) + (i * (y / x)))
    else if (x <= 6.2d-137) then
        tmp = a + (t + (z + (b * log(c))))
    else if (x <= 4.2d+80) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = a + (t + (z + (x * log(y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -4.6e+184) {
		tmp = x * (Math.log(y) + (i * (y / x)));
	} else if (x <= 6.2e-137) {
		tmp = a + (t + (z + (b * Math.log(c))));
	} else if (x <= 4.2e+80) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = a + (t + (z + (x * Math.log(y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -4.6e+184:
		tmp = x * (math.log(y) + (i * (y / x)))
	elif x <= 6.2e-137:
		tmp = a + (t + (z + (b * math.log(c))))
	elif x <= 4.2e+80:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = a + (t + (z + (x * math.log(y))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -4.6e+184)
		tmp = Float64(x * Float64(log(y) + Float64(i * Float64(y / x))));
	elseif (x <= 6.2e-137)
		tmp = Float64(a + Float64(t + Float64(z + Float64(b * log(c)))));
	elseif (x <= 4.2e+80)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -4.6e+184)
		tmp = x * (log(y) + (i * (y / x)));
	elseif (x <= 6.2e-137)
		tmp = a + (t + (z + (b * log(c))));
	elseif (x <= 4.2e+80)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = a + (t + (z + (x * log(y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -4.6e+184], N[(x * N[(N[Log[y], $MachinePrecision] + N[(i * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e-137], N[(a + N[(t + N[(z + N[(b * N[Log[c], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+80], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.6e184

   1. Initial program 96.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 60.2%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 60.0%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around 0 60.0%

      \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{-0.5 \cdot \frac{\log c}{z}}\right)\right)\right)\right) + y \cdot i \]
   7. Step-by-step derivation

      1. associate-*r/ 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\frac{-0.5 \cdot \log c}{z}}\right)\right)\right)\right) + y \cdot i \]

      2. *-commutative 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\color{blue}{\log c \cdot -0.5}}{z}\right)\right)\right)\right) + y \cdot i \]

   8. Simplified 60.0%

      \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\frac{\log c \cdot -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   9. Taylor expanded in x around inf 79.7%

      \[\leadsto \color{blue}{x \cdot \log y} + y \cdot i \]

   10. Taylor expanded in x around inf 79.6%

       \[\leadsto \color{blue}{x \cdot \left(\log y + \frac{i \cdot y}{x}\right)} \]
   11. Step-by-step derivation

       1. associate-/l* 82.7%

          \[\leadsto x \cdot \left(\log y + \color{blue}{i \cdot \frac{y}{x}}\right) \]

   12. Simplified 82.7%

       \[\leadsto \color{blue}{x \cdot \left(\log y + i \cdot \frac{y}{x}\right)} \]

   if -4.6e184 < x < 6.19999999999999955e-137

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 85.0%

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} \]

   4. Taylor expanded in b around inf 81.5%

      \[\leadsto a + \left(t + \left(z + \color{blue}{b \cdot \log c}\right)\right) \]
   5. Step-by-step derivation

      1. *-commutative 81.5%

         \[\leadsto a + \left(t + \left(z + \color{blue}{\log c \cdot b}\right)\right) \]

   6. Simplified 81.5%

      \[\leadsto a + \left(t + \left(z + \color{blue}{\log c \cdot b}\right)\right) \]

   if 6.19999999999999955e-137 < x < 4.20000000000000003e80

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.6%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in z around inf 75.7%

      \[\leadsto \left(a + \left(t + \color{blue}{z}\right)\right) + y \cdot i \]

   if 4.20000000000000003e80 < x

   1. Initial program 99.6%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.9%

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} \]

   4. Taylor expanded in x around inf 73.7%

      \[\leadsto a + \left(t + \left(z + \color{blue}{x \cdot \log y}\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+184}:\\ \;\;\;\;x \cdot \left(\log y + i \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-137}:\\ \;\;\;\;a + \left(t + \left(z + b \cdot \log c\right)\right)\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+80}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+189} \lor \neg \left(x \leq 2.45 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot \left(\log y + i \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -1.5e+189) (not (<= x 2.45e+145)))
   (* x (+ (log y) (* i (/ y x))))
   (+ (* y i) (+ a (+ z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.5e+189) || !(x <= 2.45e+145)) {
		tmp = x * (log(y) + (i * (y / x)));
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-1.5d+189)) .or. (.not. (x <= 2.45d+145))) then
        tmp = x * (log(y) + (i * (y / x)))
    else
        tmp = (y * i) + (a + (z + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -1.5e+189) || !(x <= 2.45e+145)) {
		tmp = x * (Math.log(y) + (i * (y / x)));
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -1.5e+189) or not (x <= 2.45e+145):
		tmp = x * (math.log(y) + (i * (y / x)))
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -1.5e+189) || !(x <= 2.45e+145))
		tmp = Float64(x * Float64(log(y) + Float64(i * Float64(y / x))));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -1.5e+189) || ~((x <= 2.45e+145)))
		tmp = x * (log(y) + (i * (y / x)));
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -1.5e+189], N[Not[LessEqual[x, 2.45e+145]], $MachinePrecision]], N[(x * N[(N[Log[y], $MachinePrecision] + N[(i * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4999999999999999e189 or 2.45000000000000001e145 < x

   1. Initial program 98.1%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 63.3%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 63.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 63.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 63.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 63.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around 0 63.2%

      \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{-0.5 \cdot \frac{\log c}{z}}\right)\right)\right)\right) + y \cdot i \]
   7. Step-by-step derivation

      1. associate-*r/ 63.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\frac{-0.5 \cdot \log c}{z}}\right)\right)\right)\right) + y \cdot i \]

      2. *-commutative 63.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\color{blue}{\log c \cdot -0.5}}{z}\right)\right)\right)\right) + y \cdot i \]

   8. Simplified 63.2%

      \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\frac{\log c \cdot -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   9. Taylor expanded in x around inf 80.2%

      \[\leadsto \color{blue}{x \cdot \log y} + y \cdot i \]

   10. Taylor expanded in x around inf 80.2%

       \[\leadsto \color{blue}{x \cdot \left(\log y + \frac{i \cdot y}{x}\right)} \]
   11. Step-by-step derivation

       1. associate-/l* 81.8%

          \[\leadsto x \cdot \left(\log y + \color{blue}{i \cdot \frac{y}{x}}\right) \]

   12. Simplified 81.8%

       \[\leadsto \color{blue}{x \cdot \left(\log y + i \cdot \frac{y}{x}\right)} \]

   if -1.4999999999999999e189 < x < 2.45000000000000001e145

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 95.9%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in z around inf 73.7%

      \[\leadsto \left(a + \left(t + \color{blue}{z}\right)\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+189} \lor \neg \left(x \leq 2.45 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot \left(\log y + i \cdot \frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \left(\log y + i \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+79}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= x -4.8e+186)
   (* x (+ (log y) (* i (/ y x))))
   (if (<= x 9.8e+79)
     (+ (* y i) (+ a (+ z t)))
     (+ a (+ t (+ z (* x (log y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -4.8e+186) {
		tmp = x * (log(y) + (i * (y / x)));
	} else if (x <= 9.8e+79) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = a + (t + (z + (x * log(y))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (x <= (-4.8d+186)) then
        tmp = x * (log(y) + (i * (y / x)))
    else if (x <= 9.8d+79) then
        tmp = (y * i) + (a + (z + t))
    else
        tmp = a + (t + (z + (x * log(y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (x <= -4.8e+186) {
		tmp = x * (Math.log(y) + (i * (y / x)));
	} else if (x <= 9.8e+79) {
		tmp = (y * i) + (a + (z + t));
	} else {
		tmp = a + (t + (z + (x * Math.log(y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if x <= -4.8e+186:
		tmp = x * (math.log(y) + (i * (y / x)))
	elif x <= 9.8e+79:
		tmp = (y * i) + (a + (z + t))
	else:
		tmp = a + (t + (z + (x * math.log(y))))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (x <= -4.8e+186)
		tmp = Float64(x * Float64(log(y) + Float64(i * Float64(y / x))));
	elseif (x <= 9.8e+79)
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	else
		tmp = Float64(a + Float64(t + Float64(z + Float64(x * log(y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (x <= -4.8e+186)
		tmp = x * (log(y) + (i * (y / x)));
	elseif (x <= 9.8e+79)
		tmp = (y * i) + (a + (z + t));
	else
		tmp = a + (t + (z + (x * log(y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[x, -4.8e+186], N[(x * N[(N[Log[y], $MachinePrecision] + N[(i * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e+79], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(t + N[(z + N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.7999999999999999e186

   1. Initial program 96.7%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 60.2%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 60.0%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around 0 60.0%

      \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{-0.5 \cdot \frac{\log c}{z}}\right)\right)\right)\right) + y \cdot i \]
   7. Step-by-step derivation

      1. associate-*r/ 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\frac{-0.5 \cdot \log c}{z}}\right)\right)\right)\right) + y \cdot i \]

      2. *-commutative 60.0%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\color{blue}{\log c \cdot -0.5}}{z}\right)\right)\right)\right) + y \cdot i \]

   8. Simplified 60.0%

      \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\frac{\log c \cdot -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   9. Taylor expanded in x around inf 79.7%

      \[\leadsto \color{blue}{x \cdot \log y} + y \cdot i \]

   10. Taylor expanded in x around inf 79.6%

       \[\leadsto \color{blue}{x \cdot \left(\log y + \frac{i \cdot y}{x}\right)} \]
   11. Step-by-step derivation

       1. associate-/l* 82.7%

          \[\leadsto x \cdot \left(\log y + \color{blue}{i \cdot \frac{y}{x}}\right) \]

   12. Simplified 82.7%

       \[\leadsto \color{blue}{x \cdot \left(\log y + i \cdot \frac{y}{x}\right)} \]

   if -4.7999999999999999e186 < x < 9.7999999999999997e79

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 97.4%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in z around inf 75.9%

      \[\leadsto \left(a + \left(t + \color{blue}{z}\right)\right) + y \cdot i \]

   if 9.7999999999999997e79 < x

   1. Initial program 99.6%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 83.9%

      \[\leadsto \color{blue}{a + \left(t + \left(z + \left(x \cdot \log y + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} \]

   4. Taylor expanded in x around inf 73.7%

      \[\leadsto a + \left(t + \left(z + \color{blue}{x \cdot \log y}\right)\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \left(\log y + i \cdot \frac{y}{x}\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+79}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t + \left(z + x \cdot \log y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 74.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+189} \lor \neg \left(x \leq 2.45 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -2.5e+189) (not (<= x 2.45e+145)))
   (+ (* x (log y)) (* y i))
   (+ (* y i) (+ a (+ z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.5e+189) || !(x <= 2.45e+145)) {
		tmp = (x * log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-2.5d+189)) .or. (.not. (x <= 2.45d+145))) then
        tmp = (x * log(y)) + (y * i)
    else
        tmp = (y * i) + (a + (z + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -2.5e+189) || !(x <= 2.45e+145)) {
		tmp = (x * Math.log(y)) + (y * i);
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -2.5e+189) or not (x <= 2.45e+145):
		tmp = (x * math.log(y)) + (y * i)
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -2.5e+189) || !(x <= 2.45e+145))
		tmp = Float64(Float64(x * log(y)) + Float64(y * i));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -2.5e+189) || ~((x <= 2.45e+145)))
		tmp = (x * log(y)) + (y * i);
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -2.5e+189], N[Not[LessEqual[x, 2.45e+145]], $MachinePrecision]], N[(N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision] + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5000000000000002e189 or 2.45000000000000001e145 < x

   1. Initial program 98.1%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 63.3%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 63.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 63.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 63.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 63.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in b around 0 63.2%

      \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{-0.5 \cdot \frac{\log c}{z}}\right)\right)\right)\right) + y \cdot i \]
   7. Step-by-step derivation

      1. associate-*r/ 63.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\frac{-0.5 \cdot \log c}{z}}\right)\right)\right)\right) + y \cdot i \]

      2. *-commutative 63.2%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\color{blue}{\log c \cdot -0.5}}{z}\right)\right)\right)\right) + y \cdot i \]

   8. Simplified 63.2%

      \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\frac{\log c \cdot -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   9. Taylor expanded in x around inf 80.2%

      \[\leadsto \color{blue}{x \cdot \log y} + y \cdot i \]

   if -2.5000000000000002e189 < x < 2.45000000000000001e145

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 95.9%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in z around inf 73.7%

      \[\leadsto \left(a + \left(t + \color{blue}{z}\right)\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+189} \lor \neg \left(x \leq 2.45 \cdot 10^{+145}\right):\\ \;\;\;\;x \cdot \log y + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+237} \lor \neg \left(x \leq 9 \cdot 10^{+187}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= x -7.5e+237) (not (<= x 9e+187)))
   (* x (log y))
   (+ (* y i) (+ a (+ z t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -7.5e+237) || !(x <= 9e+187)) {
		tmp = x * log(y);
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if ((x <= (-7.5d+237)) .or. (.not. (x <= 9d+187))) then
        tmp = x * log(y)
    else
        tmp = (y * i) + (a + (z + t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((x <= -7.5e+237) || !(x <= 9e+187)) {
		tmp = x * Math.log(y);
	} else {
		tmp = (y * i) + (a + (z + t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if (x <= -7.5e+237) or not (x <= 9e+187):
		tmp = x * math.log(y)
	else:
		tmp = (y * i) + (a + (z + t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if ((x <= -7.5e+237) || !(x <= 9e+187))
		tmp = Float64(x * log(y));
	else
		tmp = Float64(Float64(y * i) + Float64(a + Float64(z + t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if ((x <= -7.5e+237) || ~((x <= 9e+187)))
		tmp = x * log(y);
	else
		tmp = (y * i) + (a + (z + t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[Or[LessEqual[x, -7.5e+237], N[Not[LessEqual[x, 9e+187]], $MachinePrecision]], N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision], N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5e237 or 9.00000000000000052e187 < x

   1. Initial program 97.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.8%

      \[\leadsto \color{blue}{x \cdot \log y} \]

   if -7.5e237 < x < 9.00000000000000052e187

   1. Initial program 99.8%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 91.9%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in z around inf 72.0%

      \[\leadsto \left(a + \left(t + \color{blue}{z}\right)\right) + y \cdot i \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+237} \lor \neg \left(x \leq 9 \cdot 10^{+187}\right):\\ \;\;\;\;x \cdot \log y\\ \mathbf{else}:\\ \;\;\;\;y \cdot i + \left(a + \left(z + t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 23.0% accurate, 13.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-237}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-144}:\\ \;\;\;\;y \cdot i\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+146}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a -1.8e-237) z (if (<= a 5.8e-144) (* y i) (if (<= a 4e+146) z a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -1.8e-237) {
		tmp = z;
	} else if (a <= 5.8e-144) {
		tmp = y * i;
	} else if (a <= 4e+146) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= (-1.8d-237)) then
        tmp = z
    else if (a <= 5.8d-144) then
        tmp = y * i
    else if (a <= 4d+146) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= -1.8e-237) {
		tmp = z;
	} else if (a <= 5.8e-144) {
		tmp = y * i;
	} else if (a <= 4e+146) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= -1.8e-237:
		tmp = z
	elif a <= 5.8e-144:
		tmp = y * i
	elif a <= 4e+146:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= -1.8e-237)
		tmp = z;
	elseif (a <= 5.8e-144)
		tmp = Float64(y * i);
	elseif (a <= 4e+146)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= -1.8e-237)
		tmp = z;
	elseif (a <= 5.8e-144)
		tmp = y * i;
	elseif (a <= 4e+146)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, -1.8e-237], z, If[LessEqual[a, 5.8e-144], N[(y * i), $MachinePrecision], If[LessEqual[a, 4e+146], z, a]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.79999999999999998e-237 or 5.8000000000000004e-144 < a < 3.99999999999999973e146

   1. Initial program 99.2%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 20.7%

      \[\leadsto \color{blue}{z} \]

   if -1.79999999999999998e-237 < a < 5.8000000000000004e-144

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 31.9%

      \[\leadsto \color{blue}{i \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative 31.9%

         \[\leadsto \color{blue}{y \cdot i} \]

   5. Simplified 31.9%

      \[\leadsto \color{blue}{y \cdot i} \]

   if 3.99999999999999973e146 < a

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 35.2%

      \[\leadsto \color{blue}{a} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 43.4% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.25 \cdot 10^{+145}:\\ \;\;\;\;z + y \cdot i\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= a 2.25e+145) (+ z (* y i)) (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.25e+145) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 2.25d+145) then
        tmp = z + (y * i)
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 2.25e+145) {
		tmp = z + (y * i);
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 2.25e+145:
		tmp = z + (y * i)
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 2.25e+145)
		tmp = Float64(z + Float64(y * i));
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 2.25e+145)
		tmp = z + (y * i);
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 2.25e+145], N[(z + N[(y * i), $MachinePrecision]), $MachinePrecision], N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.2499999999999999e145

   1. Initial program 99.4%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 69.6%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\frac{x \cdot \log y}{z} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right)} + y \cdot i \]
   4. Step-by-step derivation

      1. associate-/l* 69.6%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(\color{blue}{x \cdot \frac{\log y}{z}} + \frac{\log c \cdot \left(b - 0.5\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      2. sub-neg 69.6%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \color{blue}{\left(b + \left(-0.5\right)\right)}}{z}\right)\right)\right)\right) + y \cdot i \]

      3. metadata-eval 69.6%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \frac{\log c \cdot \left(b + \color{blue}{-0.5}\right)}{z}\right)\right)\right)\right) + y \cdot i \]

      4. associate-/l* 69.6%

         \[\leadsto z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \color{blue}{\log c \cdot \frac{b + -0.5}{z}}\right)\right)\right)\right) + y \cdot i \]

   5. Simplified 69.6%

      \[\leadsto \color{blue}{z \cdot \left(1 + \left(\frac{a}{z} + \left(\frac{t}{z} + \left(x \cdot \frac{\log y}{z} + \log c \cdot \frac{b + -0.5}{z}\right)\right)\right)\right)} + y \cdot i \]

   6. Taylor expanded in x around inf 49.4%

      \[\leadsto z \cdot \left(1 + \color{blue}{\frac{x \cdot \log y}{z}}\right) + y \cdot i \]
   7. Step-by-step derivation

      1. associate-*r/ 48.9%

         \[\leadsto z \cdot \left(1 + \color{blue}{x \cdot \frac{\log y}{z}}\right) + y \cdot i \]

   8. Simplified 48.9%

      \[\leadsto z \cdot \left(1 + \color{blue}{x \cdot \frac{\log y}{z}}\right) + y \cdot i \]

   9. Taylor expanded in x around 0 39.8%

      \[\leadsto \color{blue}{z + i \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 39.8%

          \[\leadsto z + \color{blue}{y \cdot i} \]

   11. Simplified 39.8%

       \[\leadsto \color{blue}{z + y \cdot i} \]

   if 2.2499999999999999e145 < a

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 86.6%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in a around inf 56.3%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 41.8% accurate, 21.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+188}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a + y \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i)
 :precision binary64
 (if (<= z -2e+188) z (+ a (* y i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2e+188) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (z <= (-2d+188)) then
        tmp = z
    else
        tmp = a + (y * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (z <= -2e+188) {
		tmp = z;
	} else {
		tmp = a + (y * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if z <= -2e+188:
		tmp = z
	else:
		tmp = a + (y * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (z <= -2e+188)
		tmp = z;
	else
		tmp = Float64(a + Float64(y * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (z <= -2e+188)
		tmp = z;
	else
		tmp = a + (y * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[z, -2e+188], z, N[(a + N[(y * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e188

   1. Initial program 100.0%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 69.8%

      \[\leadsto \color{blue}{z} \]

   if -2e188 < z

   1. Initial program 99.4%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 81.7%

      \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

   4. Taylor expanded in a around inf 38.3%

      \[\leadsto \color{blue}{a} + y \cdot i \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 16: 68.1% accurate, 24.3× speedup

Math

\[\begin{array}{l} \\ y \cdot i + \left(a + \left(z + t\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (+ (* y i) (+ a (+ z t))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + (a + (z + t));
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = (y * i) + (a + (z + t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (y * i) + (a + (z + t));
}

Python

def code(x, y, z, t, a, b, c, i):
	return (y * i) + (a + (z + t))

Julia

function code(x, y, z, t, a, b, c, i)
	return Float64(Float64(y * i) + Float64(a + Float64(z + t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = (y * i) + (a + (z + t));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := N[(N[(y * i), $MachinePrecision] + N[(a + N[(z + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Add Preprocessing

3. Taylor expanded in x around 0 82.8%

   \[\leadsto \color{blue}{\left(a + \left(t + \left(z + \log c \cdot \left(b - 0.5\right)\right)\right)\right)} + y \cdot i \]

4. Taylor expanded in z around inf 65.0%

   \[\leadsto \left(a + \left(t + \color{blue}{z}\right)\right) + y \cdot i \]

5. Final simplification 65.0%

   \[\leadsto y \cdot i + \left(a + \left(z + t\right)\right) \]
6. Add Preprocessing

Alternative 17: 21.2% accurate, 36.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3.2 \cdot 10^{+145}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 (if (<= a 3.2e+145) z a))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.2e+145) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8) :: tmp
    if (a <= 3.2d+145) then
        tmp = z
    else
        tmp = a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if (a <= 3.2e+145) {
		tmp = z;
	} else {
		tmp = a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i):
	tmp = 0
	if a <= 3.2e+145:
		tmp = z
	else:
		tmp = a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i)
	tmp = 0.0
	if (a <= 3.2e+145)
		tmp = z;
	else
		tmp = a;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i)
	tmp = 0.0;
	if (a <= 3.2e+145)
		tmp = z;
	else
		tmp = a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := If[LessEqual[a, 3.2e+145], z, a]

Derivation

1. Split input into 2 regimes

2. if a < 3.20000000000000008e145

   1. Initial program 99.4%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 19.2%

      \[\leadsto \color{blue}{z} \]

   if 3.20000000000000008e145 < a

   1. Initial program 99.9%

      \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 35.2%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 16.3% accurate, 219.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b c i) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return a;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    code = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return a;
}

Python

def code(x, y, z, t, a, b, c, i):
	return a

Julia

function code(x, y, z, t, a, b, c, i)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_] := a

Derivation

1. Initial program 99.4%

   \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i \]
2. Add Preprocessing

3. Taylor expanded in a around inf 16.2%

   \[\leadsto \color{blue}{a} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024108 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))